Great time of year. I would go in late May though. Temperatures will be a little warmer. Both cities, especially London, can even be chilly during the peak of summer. As said above, i would split the time up more evenly. Two days in London will not be enough. Five days in each city would be a good amount of time.

Not as many as you think. It is really tough for law school graduates right now because 1) there are few entry level attorney jobs and 2)they are overqualified to get a paralegal or other legal related job. Most employers won't touch a JD with a 10 foot pole because they are afraid of the person jumping ship if a better job comes along (which i don't think employers quite understand is going to be rare today).
A legal education is still good if you can go to a top 3...

Yup. Even t14 does not guarantee anything. I know plenty of people who did well at t14 schools and are still struggling to find employment. Also, even if you finish in the top 5 % at a regional school expect to make 50k or less if you are even lucky enough to be employed at all (about a 50/50 chance of employment).
In summation, don't go to law school. I don't see legal employment being much better in a few years. You are probably better off trying paralegal work. He'll,...